Nuclear magnetic resonance pulse sequence for optimizing instrument electrical power usage

ABSTRACT

A method for acquiring nuclear magnetic resonance measurements of a material uses a gradient tool. A modified CPMG sequence is used wherein the duration of the refocusing pulse is selected to maximize the SNR of the pulse echoes relative to a standard CPMG sequence in which the refocusing pulse has twice the duration of the tipping pulse. The results of using the shortened refocusing pulse with reduced power requirements are comparable to those obtained with a conventional CPMG sequence.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The invention is related to the field of nuclear magneticresonance (“NMR”) apparatus and methods. More specifically, theinvention is related to methods for conducting NMR measurements in amanner which optimizes the use of electrical power by the NMR instrumentand obtains results comparable to those obtained with prior art pulsesequences.

[0003] 2. Description of the Related Art

[0004] NMR instruments adapted for well logging can be used fordetermining, among other things, the fractional volume of pore space andthe fractional volume of mobile fluid filling the pore space of earthformations. Methods for using NMR well logging measurements fordetermining the fractional volume of pore space and the fractionalvolume of mobile fluids are described, for example, in, Spin EchoMagnetic Resonance Logging: Porosity and Free Fluid Index Determination,M. N. Miller et al, Society of Petroleum Engineers paper no. 20561,Richardson, Tex. (1990).

[0005] NMR well logging instruments known in the art are typicallydesigned to make measurements corresponding to an amount of time forhydrogen nuclei present in the earth formation to realign their spinaxes, and consequently their bulk magnetization, either with anexternally applied static magnetic field, or perpendicularly to themagnetic field, after momentary reorientation of the nuclear spin axes.The externally applied magnetic field is typically provided by apermanent magnet disposed in the NMR instrument. The spin axes of thehydrogen nuclei in the earth formation, in the aggregate, become alignedwith the static magnetic field induced in the earth formation by thepermanent magnet. The NMR instrument also includes an antenna positionednear the magnet and shaped so that a pulse of radio frequency (RF) powerconducted through the antenna induces a corresponding RF magnetic fieldin the earth formation in a direction orthogonal to the static fieldinduced by the permanent magnet. This RF pulse (called an “A-pulse”hereafter) has a duration and amplitude selected so that the spin axesof the hydrogen nuclei generally align themselves perpendicular both tothe RF magnetic field and to the static magnetic field. After theA-pulse ends, the nuclear magnetic moment of the hydrogen nucleigradually “relax” or return to their alignment with the static magneticfield. The amount of time taken for this relaxation is related to theproperties of interest of the earth formation.

[0006] Also after the A-pulse ends, the antenna is typicallyelectrically connected to a receiver, which detects and measuresvoltages induced in the antenna by precessional rotation of the spinaxes of the hydrogen nuclei. While the hydrogen nuclei gradually realigntheir spin axes with the static magnetic field, they do so at differentrates because of inhomogeneities in the magnet's field and because ofdifferences in the chemical and magnetic environment within the earthformation. Different rates of realignment of the spin axes of thehydrogen nuclei result in a rapid decrease in the voltage induced in theantenna. The rapid decrease in the induced voltage is referred to as thefree induction decay (FID).

[0007] After a predetermined time period following the FID, another,longer RF pulse (called a “B-pulse” hereafter) is applied to theantenna. The B-pulse has a duration and amplitude selected to reorientthe spin axes of the hydrogen nuclei in the earth formation by an axialrotation of 180° from their immediately previous orientations. After theB-pulse, hydrogen nuclear spin axes that were realigning with theexternally applied field at a slower rate then are positioned so thatthey are “ahead” of the faster realigning nuclear spin axes. This causesthe faster realigning axes to be positioned “behind” the slowerrealigning spin axes. The faster realigning spin axes then eventually“catch up” to, and come into approximate alignment with, the sloweraligning spin axes at some time after the B-pulse. As a large number ofthe spin axes become aligned with each other, the hydrogen nuclei againare able to induce measurable voltages in the antenna. The voltagesinduced as a result of realignment of the hydrogen nuclear spin axeswith each other after a B-pulse is referred to as a “spin echo”. Thevoltage induced by the spin echo is typically smaller than the originalFID voltage induced after cessation of the A-pulse, because theaggregate nuclear axial alignment, and consequently the bulkmagnetization, of the hydrogen nuclei at the time of the spin echo is atleast partially realigned with the static magnetic field and away fromthe sensitive axis of the antenna. The spin echo voltage itself rapidlydecays by FID as the faster aligning nuclear axes again “dephase” fromthe slower aligning nuclear axes.

[0008] After another period of time equal to two of the predeterminedtime periods between the A-pulse and the first B-pulse, another B-pulseof the same amplitude and duration as the first B-pulse can be appliedto the antenna. This next B-pulse again causes the slower realigningspin axes to be positioned ahead of the faster realigning axes, andeventually another spin echo will induce voltages in the antenna. Thevoltages induced by this next spin echo will typically be smaller thoseinduced by the previous spin echo.

[0009] Successive B-pulses are applied at regular time intervals to theantenna to generate successive spin echoes, each one typically having asmaller amplitude than the previous spin echo. The rate at which thepeak amplitude of the spin echoes decreases is related to the propertiesof interest of the earth formation, such as the fractional volume ofpore space or the fractional volume of mobile fluid filling the porespace. The number of spin echoes needed to determine the rate of spinecho amplitude decay is related to the properties of the earthformation. In some cases as many as 1,000 spin echoes may be needed todetermine the amplitude decay corresponding to the particular formationproperties of interest.

[0010] A limitation of NMR well logging instruments using thejust-described RF pulse sequence is that this pulse sequence uses a verylarge amount of electrical power. Typically the DC power requirement forthe NMR logging instruments known in the art is about 1 KW; the peakpower required for effective nuclear excitation can be as high as 30 KWin each pulse. As is known in the art, a typical well logging cable hasa power transmission capacity of about 1.5 KW. Using NMR pulse sequencesknown in the art it is impractical to increase the RF power in order toimprove signal to noise or to increase the axial speed (“logging speed”)at which the instrument is moved through the wellbore (the increasedspeed being desired by the wellbore operator to save operating time andassociated costs). It is also impractical to combine NMR well logginginstruments using pulse sequences known in the art with other welllogging instruments because the NMR logging instrument uses nearly theentire power transmission capacity of the typical well logging cable.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011]FIG. 1 (PRIOR ART) shows a simulated spin echo train for B-pulseflip angles of 180°, 120° and 90° when the flip angle induced byB-pulses is selected by varying the amplitude of the B-pulses.

[0012]FIG. 2 (PRIOR ART) shows a graph of SNR of “stacked” spin echotrains having varying B-pulse durations, but the same overall powerconsumption as a single 180° B-pulse spin echo train, normalized to theSNR of the single 180° B-pulse echo train.

[0013]FIG. 3 (PRIOR ART) shows the DC power consumption of the stackedspin echo trains having varying B-pulse durations, but the same SNR,normalized to the power consumption of a single 180° B-pulse echo train.

[0014]FIG. 4 (PRIOR ART) shows simulated echo trains where the flipangle induced by B-pulses is selected by varying the duration of theB-pulses.

[0015]FIG. 5 (PRIOR ART) shows the SNR of stacked echo trains simulatedas in FIG. 4 with respect to the flip angle of the B-pulses, normalizedto the SNR of a single echo train having a B-pulse flip angle of 180°.

[0016]FIG. 6 (PRIOR ART) shows the DC power consumption of the stackedecho trains simulated as in FIG. 4 with respect to the flip angle of theB-pulses, normalized to the DC power consumption of a single echo trainhaving a B-pulse flip angle of 180°.

[0017]FIG. 7 (PRIOR ART) shows a graph of correction coefficients foreach of the first 20 echoes in an echo train for B-pulse flip angles of180°, 120° and 90°, where the value of T₂ is selected to be 10, 100 and1,000 milliseconds for each flip angle.

[0018]FIG. 8 (PRIOR ART) shows the dependence of the pulse echo signaland the SNR of the pulse echo signal on the duration of the B-pulse.

[0019]FIG. 9 shows an arbitrary two pulse NMR sequence with excitationpulse of length τ_(a), refocusing pulse of length τ_(b), and pulsespacing τ. Free induction decays and a spin echo decay are also shown.

[0020]FIG. 10 shows an arbitrary three pulse NMR sequence along with theechoes that result from the sequence.

[0021]FIG. 11 shows the initial portion of a Carr-Purcell spin echosequence. The upper line shown the Hahn spin echoes, the middle lineshows the stimulated echoes, and the bottom line shows examples ofindirect echoes.

[0022]FIG. 12 shows a graph of Apparent Relaxation Times for materialswith different ratios of T₁/T₂ ranging from 1 to 100. Results are shownfor flipping angles of 90°, 135°, and 180°.

[0023]FIG. 13 shows a graph of Percent Error of Relaxation Times forflipping angles of 90°, 135°, and 180° at the same ratios of T₁/T₂ asused in FIG. 9.

[0024]FIG. 14 shows an application sequence of CPMG sequences for thefirst embodiment of the invention.

[0025]FIG. 15 shows an application sequence of CPMG sequences for thesecond embodiment of the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENT

[0026] The method of acquiring NMR pulse echo data using shortenedrefocusing pulses has been described in U.S. Pat. No. 6,163,153 toReiderman et al, the contents of which are fully incorporated herein bereference. Much of the material that follows immediately thereafterrelating to the use of shortened refocusing pulses has been described inthe Reiderman patent.

[0027] A typical nuclear magnetic resonance (“NMR”) instrument that canmake measurements according to this invention is described, for example,in U.S. Pat. No. 5,585,720 issued to Edwards. The instrument describedin the Edwards '720 patent includes a permanent magnet for inducing astatic magnetic field within the materials to be analyzed. Inparticular, the materials to be analyzed can include earth formationssurrounding a wellbore. The instrument in the Edwards '720 patentincludes an antenna coil which can be wound around the magnet, circuitryfor applying pulses of radio-frequency (RF) power to the antenna coil,and circuitry for detecting voltages induced in the antenna coil as aresult of nuclear magnetic resonance phenomena, particularly that ofhydrogen nuclei present in the earth formations.

[0028] As is known in the art, the RF pulses applied to the antenna coilof NMR apparatus such as the one in Edwards typically include an initialRF pulse having a duration and amplitude which reorients the nuclearspin axes of the hydrogen nuclei in the earth formations so that theybecome substantially perpendicular to the direction of the staticmagnetic field induced by the magnet. This first RF pulse (hereafter“A-pulse”) is said to induce an angular deflection of about 90° in thespin axes of the hydrogen nuclei. Later in the measurement cycle knownin the art, a sequence of additional RF pulses (referred to as“B-pulses”), each of these B-pulses having a duration and amplitudeselected to reorient the extant nuclear spin axes by about 180°, is thenapplied to the antenna coil. In between B-pulses, the antenna coil isconnected to a receiver circuit to detect voltages induced in theantenna coil as the nuclear spin axes “rephase”, an event called thepulse-echo or spin echo. The combination of A-pulse and 180 degreeB-pulses is known as a Carr-Purcell-Meiboom-Gill (CPMG) sequence.

[0029] U.S. Pat. No. 5,023,551 issued to Kleinberg discloses an NMRpulse sequence for use in the borehole environment which combines amodified fast inversion recovery (FIR) pulse sequence with a series ofmore than ten, and typically hundreds, of CPMG pulses according to

[W _(i)−180_(x) −t _(i)−90_(x)−(t _(cp)−180_(y) −t_(cp)−echo)_(J)]_(i)  (1)

[0030] where j=1, 2, . . . , J, and J is the number of echoes collectedin a single CPMG sequence, where i=1, 2, . . . , I and I is the numberof waiting times used in the pulse sequence, where W_(i) are therecovery times before the inversion pulse, and where t_(i) are therecovery times before a CPMG sequence, and where t_(CP) is theCarr-Purcell spacing. The phase of the RF pulses 90 and 180 is denotedby the subscripts X and Y, Y being phase shifted by π/2 radians withrespect to X. The subscripts also conventionally relate to the axisabout which rotation of the magnetization occurs during the RF pulse ina local Cartesian co-ordinate system centered on the nucleus in whichthe static magnetic field is aligned in the Z direction and the RF fieldin the X direction. This sequence can be used to measure both T₁ and T₂,but is very time consuming, limiting logging speed. If t_(i) is set tozero and the inverting pulse is omitted, then the sequence defaults tostandard CPMG for measuring T₂ only.

[0031] The “A” pulse or the tipping pulse in a CPMG sequence is the 90°pulse in Eq. (1) and the “B” pulse or the refocusing pulse in a CPMGsequence is 180°.

[0032] As is understood by those skilled in the art, the amplitude ofthe induced voltages from spin rephasing (pulse-echo voltages) decreasesafter each successive B-pulse applied to the antenna coil. The rate atwhich the amplitude of the successive pulse-echo voltages decays isrelated to properties of the earth formations such as fractional volumeof pore space and the bulk volume of mobile fluids filling the porespace, as is known in the art.

[0033] In the invention, it has been determined that the B-pulses can,and preferably do, have a duration and amplitude selected to cause thenuclear spin axes to reorient by an angular deflection different from180°. FIG. 1 shows a simulated spin echo “train” (the magnitude of thevoltages induced in the receiver coil for each of the spin echoes) forB-pulse angular reorientation (hereafter referred to as the “flip”angle) of 180°, 120° and 90°, at curves 10, 12, and 14, respectively.What is apparent from FIG. 1 is that the average amplitude of the spinechoes is reduced only by about 30 percent (although the first andsecond echoes are reduced in amplitude substantially more than this) byreducing the flip angle of the B-pulses from 180° to 90°.

[0034] Reducing the flip angle of the B-pulses from 180° to 90°,however, reduces the amount of electrical power consumed in generatingthe B-pulses by about 75 percent. The reduction in electric powerconsumption makes possible generation of additional spin echomeasurement sequences using the same overall amount of electrical power.These additional spin echo measurement sequences can be summed or“stacked” to improve the signal to noise ratio (“SNR”) over that of asingle CPMG sequence using 180° B-pulses, while using the same overallamount of electrical power.

[0035] For example, four spin echo trains each having a 90° flip angleB-pulses could be used, these sequences in total consuming the sameoverall electrical power as a single spin echo train having 180° flipangle B-pulses. The four echo trains can then be stacked. The signal tonoise ratio (“SNR”) of the four stacked spin echo trains would be twice(square root of four) that of a single spin echo train having 90°B-pulses. Four, stacked spin echo trains having 90° B-pulses would haveSNR about 50 percent more than a single spin echo train having 180°B-pulses, owing to the amplitude reduction of the individual spin echoesof about 30 percent for 90° B-pulse spin echoes as compared to 180°B-pulse spin echoes. It should be noted that each spin echo train hasonly one A-pulse, so the A-pulse duration and amplitude do notmaterially affect the overall electrical power consumption because thetypical spin echo train includes about 500 to 1,000 B-pulses, as isknown in the art. Another example spin echo train measurement sequencecan include stacking only three spin echo trains each having 90°B-pulses. This measurement technique would both reduce electrical powerconsumption and modestly increase overall SNR as compared to a singleecho train having 180° B-pulses.

[0036] Acquiring multiple spin echo trains for summing or stacking canbe done in a number of different ways. One way would be to wait for anamount of time between spin echo measurement sequences of about 5 timesthe T₁ value, to allow nuclei in the medium surrounding the instrumentto reorient along the static magnetic field. As is understood by thoseskilled in the art of well logging, waiting for nuclear spinreorientation along the static magnetic field would make the overallmeasurement technique relatively slow. Therefore, another technique foracquiring multiple measurement sequences for stacking can be performedusing an instrument such as one described in U.S. Pat. No. 5,712,566issued to Taicher et al, the contents of which are incorporated hereinby reference. The instrument described in Taicher et al can make NMRmeasurements at a plurality of different radio frequencies. Because themagnet in that instrument induces a static magnetic field having anamplitude gradient, making NMR measurements at different frequencieswould cause nuclear magnetic excitation in different excitation volumes.This would eliminate the need to wait between measurement sequencessince nuclear reorientation in one excitation volume would notmaterially affect measurements made in a different excitation volume.

[0037] In more general terms, if noise in the measurements is normallydistributed, it is possible to determine an optimal flip angle, α, forthe spin echo train for any given DC (average) by maximizing the value:$\begin{matrix}{\frac{180}{a} \cdot \frac{S_{a}}{S_{180}}} & (2)\end{matrix}$

[0038] where S₁₈₀ represents the SNR for the signals acquired using aconventional flip angle of S₁₈₀ and S_(α) represents the SNR for thesignals acquired using a flip angle α. The foregoing description ofstacking a number of echo trains to improve SNR while maintaining thesame overall power usage is not the only possible way to acquire NMRmeasurements using the method of this invention. As previouslyexplained, the overall amplitude (and consequently SNR) of the spinechoes in a single echo train using 90° B-pulses, for example, isreduced by about 30 percent from a spin echo train using 180° B-pulses.However, in the same example, the power used in generating the echotrain using 90° B-pulses is reduced by about 75 percent from that neededto generate the echo train using 180° B-pulses. Using an expression suchas that in equation (1), NMR measurements can be made using single echotrains wherein the flip angle is selected to optimize the SNR withrespect to the amount of power used to generate the spin echo train.This can result in reduced power usage for a given SNR, or may alsoallow the system designer to use single echo train measurements whereinthe power usage is minimized while maintaining an acceptable SNR for themeasurements.

[0039]FIG. 2 shows SNR of spin echoes in summed or “stacked” echo trainshaving varying B-pulse flip angles, the SNR being normalized to the SNRof a single echo train having 180° flip angle B-pulses. The number ofecho trains stacked for each of the various flip angles is calculated tohave the same overall DC power consumption as the single echo trainhaving 180° B-pulses. The SNR for some of the individual spin echoes inthe “stacked” echo train is shown with respect to the selected B-pulseflip angle. It should be noted that the SNR for these individual echoesrepresents the stacked value, where the number of these sameindividually indexed spin echoes in each of the echo trains is equal tothe total number of echo trains which is summed. For purposes ofcalculating the curves shown in 90°, the number of stacked echo trainscan be represented by the expression: $\begin{matrix}{N = \sqrt{\frac{P_{\alpha}}{P_{180}}}} & (3)\end{matrix}$

[0040] where N represents the number of stacked echo trains, P_(α)represents the power consumed by each spin echo train having B-pulses offlip angle α, and P₁₈₀ represents the power consumed by a spin echotrain having 180° B-pulses. As a practical matter, however, an integral(whole) number of spin echo trains (N) for the selected B-pulse flipangle will most likely stacked for actual spin echo measurements made bya logging instrument in a wellbore.

[0041] As can be observed in FIG. 2, for the second through the ninthspin echoes, shown as curves 22 through 36, respectively, the stackedSNR is generally greater than that in a corresponding single echo trainhaving 180° B-pulses. As a group, these individual echoes peak instacked SNR at about 90° to 110°. The first echo, shown at curve 22, issubstantially different, having stacked SNR of about 58 percent of a180° spin echo at a flip angle of 40°, with SNR peaking at about 120°to140°. Using a selection criterion that the stacked first spin echoesshould have SNR at least equal to that of a single spin echo train using180° flip angle B-pulses, it can be inferred that B-pulse flip angles inthe range of about 80° to 120° will provide substantially improved SNRwith respect to an echo train having 180° B-pulses, while having thesame DC power consumption to generate the B-pulses as that needed togenerate a single echo train having 180° B-pulses. It should be notedthat the graph in FIG. 2 assumes that the particular B-pulse flip angleis selected by selecting the amplitude of the B-pulses. The duration ofthe B-pulses remains substantially constant. The converse case where theB-pulse amplitude is maintained constant and the duration is varied toselect the flip angle will be further explained.

[0042]FIG. 3 shows the DC power consumption used in generating B-pulseshaving the same varying flip angles as shown in FIG. 2, normalized tothe DC power consumption used for generating a single 180° B-pulse echotrain, where the SNR for each of the types of spin echo trains is heldsubstantially constant. Similarly as in the results shown in FIG. 2, forB-pulse flip angles in a range of about 80°to 120° the specific DC powerconsumption for generating the B-pulses is most reduced from that usedto generate B-pulses having a flip angle of 180°.

[0043] The flip angle induced by the B-pulses can also be selected byvarying the duration of the B-pulses while maintaining a substantiallyconstant B-pulse amplitude. An echo train simulation similar to the oneshown in FIG. 1 is shown in FIG. 4, where the amplitudes of spin echoesare shown for flip angles of 180°, 120° and 90° at curves 40, 42, and44, respectively. In the simulation results shown in FIG. 5, the B-pulseflip angle is selected by adjusting the B-pulse duration whilemaintaining the amplitude substantially constant. Corresponding SNRcurves with respect to the B-pulse flip angle are shown in FIG. 5 forthe first echo at curve 50, the second echo at curve 52 and the thirdecho at curve 54. Fourth through ninth echoes are shown as a group ofcurve 56. As can be observed in FIG. 5, the SNR for the first echo 50has a “plateau”-like maximum in a range of about 100° to 160°. Thesecond echo 52 has a peak SNR in the range of about 95-115°. In thegraph of FIG. 5, the receiver bandwidth is set to an amountcorresponding to the spin echo signal spectrum. The bandwidth isinversely proportional to the pulse width angle

[0044] The DC power consumption normalized to that of 180°-durationB-pulses, for the simulated spin echoes shown in FIG. 4, is shown inFIG. 6. The first echo 60 has a minimum power consumption in a range ofabout 100°to 160°. The second echo 62 has a minimum power consumption ina range of about 95-115°.

[0045] It should be noted that reducing the B-pulse width to select theflip angle may affect the necessary width of the A-pulse. Inconventional NMR spin echo measurements the B-pulses have a duration ofabout twice that of the A-pulses. If the B-pulse flip angle is reducedby selecting a reduced pulse duration, it may be necessary tocorrespondingly reduce the A-pulse width (but correspondingly increasethe A-pulse amplitude to maintain a 90°flip angle) to avoid thesituation where the A-pulse does not equally excite all the nuclearmagnetic spins which will then be affected by the B-pulses. This effectwould spoil any possible signal to noise improvement offered by themethod of the invention unless the A-pulse width is reduced toapproximately one-half the B-pulse width.

[0046] To summarize, using an expression similar to that of equation(1), a B-pulse flip angle can be selected for NMR spin echo measurementsequences which provides a maximum SNR while minimizing the use ofelectrical power by the instrument.

[0047] As is known in the art, NMR well logging measurements as apractical matter are not conducted in a perfectly homogeneous staticmagnetic field. The NMR signals detected by the typical well logginginstrument will therefore have a non-zero bandwidth. A consequence ofthe bandwidth of the NMR signals is that the spin echo peak amplitudesdo not precisely correspond to the theoretical spin echo amplitudeswhich would obtain for given earth formation properties if the staticmagnetic field had zero gradient. The magnitude of the effect of signalbandwidth on the spin echo amplitudes is well known. As is known in theart, a correction coefficient can be defined for each spin echo toadjust its amplitude to the theoretical value which would obtain in azero gradient static magnetic field. This is shown by the followingexpression: E_(j)^(c) = K_(j) ⋅ E_(j)^(m)

[0048] where E^(c) _(j) represents the corrected amplitude of the j-thspin echo, K_(j) represents the j-th correction factor, and E^(m) _(j)represents the j-th measured spin echo amplitude. For the typical NMRwell logging instrument, a series of correction factors can bedetermined for each of the j spin echoes in any measurement sequence. Inthe case where T1=T2, the values of the correction factors K_(j) are notdependent on T2. Therefore the same set of correction factors can beused for any set of spin echo measurements when T1=T2.

[0049] It has been determined that similar correction factors can bedetermined for spin echoes in an echo train where the rephasing pulses(B-pulses) have a flip angle other than 90°, which type of echo train isparticularly shown in this invention. Referring to FIG. 7, three sets ofcurves are shown, each set representing the value of the correctionfactor for particular spin echoes. The value of the correction factorfor a B-pulse flip angle is shown in curve set 74. Curve set 74 actuallyrepresents three individual curves of correction factor with respect toecho number where the T2 (and T1) value for each individual curve in theset 74 is 10, 100 and 1,000 milliseconds. Set 74 appears as only onecurve because the correction factors are essentially independent of T2.Similarly for B-pulse flip angles of 120°, shown in set 72, and 90°,shown in set 70, the values of the correction factors do not change withchanges in T2.

[0050] The curve sets 70, 72, 74 in FIG. 7 suggest that a different setof correction factors must be determined for each particular value offlip angle, bandwidth and T1/T2 ratio. The values of correction factorsare pre-calculated just once and can be stored in look up tables, forexample, for performing corrections. Therefore this invention does notrequire any specialized processing as compared to traditional correctionprocedures where the B-pulse flip angle is 180°.

[0051] Reduction of the B-pulse duration leads to an increase ofexcitation volume in an NMR device using a gradient magnetic field. Thisis due to the fact that a shorter pulse has a larger bandwidth and hencewould, in a gradient field, refocus spins from a larger volume. Thislarger volume would lead to a larger signal level. Those versed in theart would recognize that the corresponding increase in receiverbandwidth needed to take advantage of the increased bandwidth will leadto an increase in the noise level in the receiver by a factor {squareroot}(Δf). As a result, the increase in the signal due to the increasedbandwidth may not compensate for the increased noise and the SNR willdrop even though the signal level itself will go up with reduction ofthe refocusing pulse duration.

[0052] Turning now to FIG. 8, the result of changing the duration of therefocusing pulse in a CPMG sequence are illustrated. The abscissa is theduration of the refocusing pulse expressed in terms of the flip angle indegrees. The signal level is given by 101 and, as discussed above,increases as the duration of the B-pulse is reduced. As a matter offact, it is still increasing when the flip angle of the B-pulse isreduced to 60°. The SNR is given by 103 and, for the field configurationused in the simulation, has a maximum around 130°. For the display inFIG. 8, relaxation amplitude SNR is chosen to represent the SNR in thesteady state region corresponding to pulse echo 3 or later. Thesimulation results shown in FIG. 3 assume, without being a limitation,no relaxation of the spins: comparable results will occur if relaxationis included in the modeling.

[0053] It is clear from the results presented in FIG. 8 that thereduction of the flip angle of the B-pulse to 130°increases SNR by about5% compared to prior art CPMG sequences with a 180°refocusing pulse witha reduction in DC power consumption by about 30% since the DC powerconsumption is proportional to the duration of the refocusing pulse whenits amplitude is held constant. By reducing the refocusing pulse to 90°,the power consumption is reduced by 50% with only a 5% drop in SNR.

[0054] The discussion about improved signal level with reduced durationof the B-pulse is valid if and only if the spectrum of the A-pulse isbroader than the spectrum of the B-pulse: the B-pulse cannot refocusspins that have never been tipped in the first place. Hence in apreferred embodiment of the invention, the B-pulse duration should bebetween about 1.3-2.0 times the A pulse duration while maintaining the Apulse amplitude to maintain a 90° rotation angle.

[0055] To understand the importance of the invention, it is necessary tounderstand the mechanism for producing echoes. Consider an on-resonancetwo-pulse NMR in a laboratory NMR apparatus as shown in FIG. 9. As shownin this figure, the excitation pulse 901 has time duration of τ_(A) andthe refocusing pulse 902 has a time duration of τ_(B). The two pulsesare separated by the time duration τ, which represents the length oftime between the tail edge of the excitation pulse and the front edge ofthe refocusing pulse. Both excitation and refocusing pulses areaccompanied by a free induction decay 903. A spin echo 904 occurs asexpected at a time interval τ after the refocusing pulse. The amplitudeof the echo is proportional to${{\frac{1}{2}\left\lbrack {1 - {\cos \left( {\gamma \quad B_{1}\tau_{B}} \right)}} \right\rbrack}{\sin \left( {\gamma \quad B_{1}\tau_{A}} \right)}} = {{\sin^{2}\left( {\gamma \quad B_{1}{\tau_{B}/2}} \right)}{\sin \left( {\gamma \quad B_{1}\tau_{A}} \right)}}$

[0056] where B₁ is the RF magnetic field amplitude in the rotatingframe, and γ is the gyromagnetic ratio of the probe nucleus. The probenucleus is normally the proton (hydrogen) for oil well loggingapplications. In the narrow pulse approximation, this pulse sequencewill produce a spin echo regardless of the flip angles of the excitationpulse or the refocusing pulse except under some very limitedcircumstances. If the first pulse produces a flip angle of exactly nπ,then the amplitude of the echo is zero. The maximum amplitude occurswhen the flip angles for the A and B pulses are 90° and 180°respectively. In practice, the flip angle is never perfect over theentire sample because of spatial inhomogeneities in either the static orthe RF magnetic field and any two pulses produce an echo regardless ofthe pulse length.

[0057] The statement can be generalized to say that any pair of pulseswithin an arbitrary pulse sequence will produce an echo. It occurs at atime such that the time interval between the echo and the second pulseequals the time interval between the first and second pulse.Furthermore, the second half of an echo can be considered the freeinduction decay of a phantom pulse at the center of the echo. Thus, anecho-pulse pair will also produce an echo with the time interval betweenthe first echo and the pulse being equal to the time interval betweenthe pulse and the second echo.

[0058] In a three-pulse sequence, there are five echoes produces, asseen in FIG. 10. The first echo shown is identical in origin to the echoin FIG. 9. The four remaining echoes follow the third pulse in thesequence. If τ₁ is the time interval between the first and second pulseand τ₂ is the time interval between the second and third pulse, theechoes occur at the following times: 2τ₁+τ₂, 2τ₂, 2τ₁+2τ₂, and τ₁+2τ₂.The earliest of these echoes (1-2-3) is produced by all three RF pulsesand is known as the stimulated echo. When the pulse flip angles areoptimum, its amplitude is 50% of the Hahn spin echo. The magnetizationresponsible for it evolves for a time τ₁ in the xy-plane, then evolvesfor a time τ₂ in the z-direction. The third pulse tips the magnetizationinto the xy-plane again where it evolves for another time τ₁ beforeforming another echo. Pairs of events generate the three remainingechoes. The free induction decays from the first two pulses incombination with third pulse generate two echoes. The final echo (1-3)is the second Hahn spin echo. It is generated by the echo-third RF pulsepair (Echo-3).

[0059] When the time intervals between the three pulses shown in FIG. 10are the special case of a Carr-Purcell pulse train, then stimulated echoand the Hahn spin echo are coincident at 2τ₂. The echo labeled 2-3 inthe figure occurs at 2.5τ₂ and the echo labeled 1-3 occurs at 3τ₂. In aCarr-Purcell echo train the 2-3 echo will occur at the time of thefourth RF pulse and contribute to its free induction decay. Echo 1-3will occur at the position of the third spin echo.

[0060]FIG. 11 shows the initial portion of a Carr-Purcell spin echosequence. The phases of the pulses are not given, so the sequence couldbe any variation of the Carr-Purcell sequence such as aCarr-Purcell-Meiboom-Gill sequence or a phase-alternate Carr-Purcellsequence. This figure illustrates the evolution of the magnetizationthat forms the different echoes. The upper line 1101 shows the formationof Hahn spin echoes. These echoes arise from that fraction of themagnetization that has evolved purely in the transverse or xy-plane inthe rotating frame. The second line 1102 shows stimulated echoes. Whatdifferentiates stimulated echoes from Hahn echoes is the fact that theyare comprised of the magnetization that has evolved in the longitudinal(or z) direction between all the pulses except in the interval betweenthe initial excitation and refocusing pulses as well as the intervalfrom the pulse prior to the echo and the echo itself. Indirect echoes1103 are those echoes that evolve to varying degrees in the transverseand longitudinal direction. Shown in this figure are those echoes thatevolve for one TE interval in the longitudinal direction. The firstindirect echo (labeled xy-xy-z-xy/xy-z-xy-xy) is formed at 3 TE afterthe third refocusing pulse. The second indirect echo that forms at 4 TEis the combination of three different echoes. The labels in theillustration indicate that the three echoes evolve in the longitudinaldirection during the first, second, and third TE intervals respectively.At 4 TE another set of indirect echoes will also form, although they arenot illustrated. These echoes evolve for 2 TE in the longitudinaldirection instead of just one.

[0061] The usefulness of standard CPMG sequences in estimating earthformation properties is well documented. It is necessary for thejustification of the preferred embodiments that values obtainedreasonably approximate those values obtained by standard CPMG sequences.FIG. 12 shows the results of a simulation of the Bloch equation toillustrate the effect of T₁/T₂ on the apparent relaxation time in a lowflip-angle pulse sequence. The simulation covers a T₁/T₂ ratio thatspans the range of expected ratios from fluids, including the formationbrine, light to heavy oils, and natural gas. Results are shown for flipangles of 180° (1201), 135° (1202), and 90° (1203). The figure showsthat a 90° B pulse gives values that are close to those obtained via the180° B pulse.

[0062] It is noteworthy as can be seen in FIG. 12 that although valuesof the apparent relaxation time obtained for a 90° B pulse and for a135° B pulse drift to higher relaxation times for higher T₁/T₂ ratios,the same occurs for the 180° flipping pulse. In a narrow pulseapproximation, it is expected that the 180° pulse would hold a constantrelaxation rate at all T₁/T₂ ratios, but since the narrow pulseapproximation does not hold in NMR well logging tools, the relaxationrate as measured with 180° B-pulses experiences a drift as well.Consequently, values for the 180° B-pulse and for the 90° B-pulsereasonably approximate one another at all ratios. FIG. 13 shows thepercent error of the between relaxation rates obtained using a givenB-pulse flip-angle and the values obtained using the 180° B-pulse atthat T₁/T₂ ratio. Values again are shown for flip-angles of 180° (1301),135° (1302), and 90° (1303). The percent error in the relaxation timefor a flip-angle of 135° (1301) and a flip-angle of 180° are smallest atlow ratios of T₁/T₂ and diverges high T₁/T₂. On the other hand, thepercent error between relaxation times for a flip-angle of 90° (1303)and for a flip-angle of 180° are largest at low T₁/T₂ and converge asT₁/T₂ increases. As seen in FIG. 13, the largest deviation in values ofthe relaxation times for the 90° B pulse and the 135° pulse are within10% of the values given through the application of a 180° pulse.

[0063] The invention described herein operates in a multi-frequencymode, and thereby is able to obtain information from formation volumessituated at several different depths into the formation. The firstembodiment of the invention uses a constant wait time (TW) and aconstant echo time (TE). Wait time is the duration of time between twogiven sequences of CPMG pulses at any given depth, and echo time is theduration of time between spin echoes or, alternatively, the duration oftime between application of B pulses. An illustration of the embodimentis given in FIG. 14 and FIG. 15. In FIG. 14, the blocks represent acomplete application of a CPMG pulse sequence. Each block is applied ata specified depth at a specified time. By altering its operatingfrequency, the invention accesses volumes at different depths extendedinto the formation, labeled in the figure as 1,2,3, . . . along thevertical axis. In this sequence, the first examined volume lies closestto the device, the second volume is at the next closest depth, the thirdvolume at the next depth, etc. Frequencies are chosen so that thevolumes are non-overlapping. Once the last volume is examined, theembodiment can repeat the sequence by examining at the first depth andcontinuing through the depths. It should be noted that the number ofvolumes is limited only by the design of the NMR logging tool and notlimited by anything inherent in the present invention. In addition, thephase of the RF pulses in each CPMG sequence can be adjusted to yield apulse sequence that can be phase-cycled to eliminate various artifactsin the measurement process that are well known in the art of NMR. Dataacquired in this manner can be inverted as is well known in the art, andporosity and permeability can be estimated from well-known empiricalrelationships.

[0064]FIG. 15 shows the details of the CPMG sequence represented byblocks in FIG. 14. In FIG. 15, TE represents the time between the peaksof the spin echoes and also the time between applications of theB-pulses.

[0065] The embodiment shown in FIG. 14 also can be used to identify thevolume filled fraction of gases by using two different TEs in the pulsesequence. In the embodiment, the odd numbered sensitive volumes(numbered 1,3,5,7, . . . in FIG. 14) are assigned one TE and the evennumbered (numbered 2,4,6, . . . in FIG. 14) assigned a second TE. The TEof the first group is small enough to capture the signal from all of theformation fluids. The TE of the second group is greater than the TE ofthe first group and is large enough so that the gas signal is no longerdetectable because of diffusion. For example, consider an NMR tool suchas the MRIL. It has a radial gradient of about 17 G/cm. At 100° C. and500 psi, the gas signal has a T₂ in the range between 17 to 40 msec fora TE of 1.2 msec. For a TE of 5.0 msec, the gas signal occurs with a T₂between 1 and 3 msec and is therefore undetectable. The difference inthe signal amplitude between the 1.2 and 5.0 msec data is thehydrocarbon gas signal. Using an estimate of the hydrogen index of thegas and taking into account the gas T₁, the gas pore volume may beestimated as is well known in the art.

[0066] In the second embodiment of the invention, all pulse sequenceparameters are kept constant except for the wait time, TW, which has twovalues, short (TWS) and long (TWL). FIG. 16 illustrates the sequence ofthe application of the pulses as well as the sequence in which volumesare examined. Depths are examined in “units”. As an example, in the unitcircled in FIG. 16, the volume at the third depth is examined, followedby the volume at the fourth depth. This sequence is then repeated aftera time TWS, so that the two volumes are then examined in the same order.The order of examination of the unit is thus 3,4,3, and then 4. Thisunit is then repeated at depths 1 and 2, depths 3 and 4, depths 5 and 6,and so on. As is shown in FIG. 16, TWS is the time between the twoapplications of the CPMG sequence within a given unit at a given depth.Also, TWL is the time between the end of the last sequence at a givendepth within a given unit and the beginning of the application of thefirst sequence of the next unit at that depth.

[0067] TWL is chosen sufficiently long so that all the formation fluidsare fully polarized prior to the application of the pulse sequence. TWSis chosen so that at the moment of the application of the phasesequence, the wetting fluid, assumed to be the formation brine, is fullypolarized, but that the hydrocarbon phases are not. Subtracting the timedomain relaxation data or equivalently the T₂ domain data afterinversion identifies the signal from the hydrocarbon phases. Theremaining signal is either hydrocarbon gas or a light crude oil. Thevolumes associated with these fluids are identified based upon theircharacteristic T₂. A typical gas phase will have a T₂ in the range of 10to 100 msec, while a light crude oil may have a characteristic T₂ in therange of 300 to 700 msec. Once the signals have been identified, thevolumes are estimated by taking into account the spin-lattice relaxationtimes of the fluids and the estimated fluid hydrogen index.

[0068] Those skilled in the art will devise other embodiments of thisinvention which do not depart from the spirit of the invention asdisclosed herein. Accordingly, the invention should be limited in scopeonly by the attached claims.

1. A method of making nuclear magnetic resonance measurement of amedium, comprising: (a) magnetically polarizing nuclei in said mediumwith a static magnetic field; (b) defining at least one sensitive volumeof the medium, said at least one sensitive volume having an associatedfrequency of a radio frequency (RF) signal; (c) defining at least onepulse sequence associated with the at least one sensitive volume, saidat least one pulse sequence comprising a wait time, an excitation pulse,at least one refocusing pulse, and a time interval between theexcitation pulse and the at least one refocusing pulse, wherein the atleast one refocusing pulse has a tipping angle less than 180°; (d)acquiring NMR pulse echo data using the at least one defined pulsesequence; and (e) processing the acquired NMR pulse echo data to obtainan estimated value of a parameter of interest of the medium, saidestimated value being substantially the same as an estimated value ofthe parameter obtained using a pulse sequence with a tipping angle ofthe refocusing pulse substantially equal to 180°.
 2. The method of claim1 wherein said at least one pulse sequence further comprises at leastone additional refocusing pulse wherein a time interval betweensuccessive ones of said refocusing pulses is substantially equal totwice the time interval between the excitation pulse and the at leastone refocusing pulse.
 3. The method of claim 1 wherein the at least onesensitive volume comprises at least two sensitive volumes.
 4. The methodof claim 3 wherein the time interval between the excitation pulse andthe at least one refocusing pulse for one of the at least two sensitivevolumes is different from the time interval between the excitation pulseand the at least one refocusing pulse for another of the at least twosensitive volumes.
 5. The method of claim 1 wherein for the at least onesensitive volume the at least one pulse sequence comprises a secondpulse sequence having a wait time different from the wait time of thefirst pulse sequence.
 6. The method of claim 1 wherein the tipping angleof the at least one refocusing pulse is greater than 90°.